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Bryson of Heraclea ( el, Βρύσων Ἡρακλεώτης, ''gen''.: Βρύσωνος; fl. late 5th-century BCE) was an
ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic p ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
sophist A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ...
who studied the solving the problems of squaring the circle and calculating pi.


Life and work

Little is known about the life of Bryson; he came from
Heraclea Pontica __NOTOC__ Heraclea Pontica (; gr, Ἡράκλεια Ποντική, Hērakleia Pontikē), known in Byzantine and later times as Pontoheraclea ( gr, Ποντοηράκλεια, Pontohērakleia), was an ancient city on the coast of Bithynia in As ...
, and he may have been a pupil of
Socrates Socrates (; ; –399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no te ...
. He is mentioned in the '' 13th Platonic Epistle'', and
Theopompus Theopompus ( grc-gre, Θεόπομπος, ''Theópompos''; c. 380 BCc. 315 BC) was an ancient Greek historian and rhetorician. Biography Theopompus was born on the Aegean island of Chios. In early youth, he seems to have spent some time at Athen ...
even claimed in his ''Attack upon Plato'' that
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institutio ...
stole many ideas for his dialogues from Bryson of Heraclea. He is known principally from
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
, who criticizes his method of squaring the circle. He also upset Aristotle by asserting that
obscene language An obscenity is any utterance or act that strongly offends the prevalent morality of the time. It is derived from the Latin ''obscēnus'', ''obscaenus'', "boding ill; disgusting; indecent", of uncertain etymology. Such loaded language can be use ...
does not exist.
Diogenes Laërtius Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, ; ) was a biographer of the Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Eminent Philosophers'' is a principal sour ...
and the
Suda The ''Suda'' or ''Souda'' (; grc-x-medieval, Σοῦδα, Soûda; la, Suidae Lexicon) is a large 10th-century Byzantine encyclopedia of the ancient Mediterranean world, formerly attributed to an author called Soudas (Σούδας) or Souidas ...
refer several times to a Bryson as a teacher of various philosophers, but since some of the philosophers mentioned lived in the late 4th-century BCE, it is possible that Bryson became confused with
Bryson of Achaea Bryson of Achaea (or Bryson the Achaean; el, Βρύσων ὁ Ἀχαιός ''Vryson o Acheos'', ''gen''.: Βρύσωνος ''Vrysonos''; fl. 330 BC) was an ancient Greek philosopher. Very little information is known about him. He was said to ha ...
, who may have lived around that time.


Pi and squaring the circle

Bryson, along with his contemporary,
Antiphon An antiphon ( Greek ἀντίφωνον, ἀντί "opposite" and φωνή "voice") is a short chant in Christian ritual, sung as a refrain. The texts of antiphons are the Psalms. Their form was favored by St Ambrose and they feature prominen ...
, was the first to
inscribe {{unreferenced, date=August 2012 An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figu ...
a polygon inside a circle, find the
polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
's area, double the number of sides of the polygon, and repeat the process, resulting in a
lower bound In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an ele ...
approximation of the
area of a circle In geometry, the area enclosed by a circle of radius is . Here the Greek letter represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which origi ...
. "Sooner or later (they figured), ...
here would be Here is an adverb that means "in, on, or at this place". It may also refer to: Software * Here Technologies, a mapping company * Here WeGo (formerly Here Maps), a mobile app and map website by Here Television * Here TV (formerly "here!"), a TV ...
so many sides that the polygon ...
ould Ould is an English surname and an Arabic name ( ar, ولد). In some Arabic dialects, particularly Hassaniya Arabic, ولد‎ (the patronymic, meaning "son of") is transliterated as Ould. Most Mauritanians have patronymic surnames. Notable pe ...
be a circle." Bryson later followed the same procedure for polygons circumscribing a circle, resulting in an
upper bound In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an elem ...
approximation of the area of a circle. With these calculations, Bryson was able to approximate π and further place lower and upper bounds on π's true value. But due to the complexity of the method, he appears to have made little progress.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
criticized this method, but
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scienti ...
would later use a
method Method ( grc, μέθοδος, methodos) literally means a pursuit of knowledge, investigation, mode of prosecuting such inquiry, or system. In recent centuries it more often means a prescribed process for completing a task. It may refer to: *Scien ...
similar to that of Bryson and Antiphon to calculate π; however, Archimedes calculated the
perimeter A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several pr ...
of a polygon instead of the area.


Robert Kilwardby on Bryson's syllogism

The 13th-century English philosopher
Robert Kilwardby Robert Kilwardby ( c. 1215 – 11 September 1279) was an Archbishop of Canterbury in England and a cardinal. Kilwardby was the first member of a mendicant order to attain a high ecclesiastical office in the English Church. Life Kilwardby ...
described Bryson's attempt of proving the quadrature of the circle as a sophistical
syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...
—one which "deceives in virtue of the fact that it promises to yield a conclusion producing knowledge on the basis of specific considerations and concludes on the basis of common considerations that can produce only belief."Robert Kilwardby, ''De ortu scientiarum'', LIII, §512, pp. 272f. His account of the syllogism is as follows:


Notes


References

*Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997. *Kilwardby, Robert. ''De ortu scientiarum''. Auctores Britannici Medii Aevi IV ed. A.G. Judy. Toronto: PIMS, 1976. Published for the British Academy by the Oxford University Press. (The translation of this quote is found in: N. Kretzmann & E. Stump (eds. & trns.), ''The Cambridge Translations of Medieval Philosophical Texts: Volume 1, Logic and the Philosophy of Language''. Cambridge: Cambridge UP, 1989.) *Philosophy Dictionary definition of Bryson of Heraclea. The Oxford Dictionary of Philosophy. Copyright © 1994, 1996, 2005 by Oxford University Press. *


External links


The History of Pi
* {{DEFAULTSORT:Bryson of Heraclea Ancient Greek mathematicians 5th-century BC Greek people 4th-century BC Greek people 5th-century BC births 4th-century BC deaths Sophists 5th-century BC mathematicians